【How-to】What is integration of sinx x

Function f (x) = e−x2 sinx is absolutely integrable on (−∞,∞). Indeed, the function f is locally integrable on (−∞, ∞), a function g(x) = e−x2 is improperly integrable on (−∞, ∞), and |f (x)| ≤ g(x) for all x ∈ R. absolutely integrable on (0, 1).